As shown in the figure, in Young's double slit experiment, a thin plate of thickness $$t = 10 \mu m$$ and refractive index $$\mu = 1.2$$ is inserted infront of slit $$S_1$$. The experiment is conducted in air ($$\mu = 1$$) and uses a monochromatic light of wavelength $$\lambda = 500$$ nm. Due to the insertion of the plate, central maxima is shifted by a distance of $$x\beta_0$$. $$\beta_0$$ is the fringe-width before the insertion of the plate. The value of the $$x$$ is ______